Zunächst e = 0 einsetzen
160000a + 8000b + 400c + 20d = 80
2560000a + 64000b + 1600c + 40d = 160
256000a + 4800b + 80c + d = 0
12960000a + 216000b + 3600c + 60d = 0
I - 20*III ; II - 40*III ; IV - 60*III
- 4960000·a - 88000·b - 1200·c = 80
- 7680000·a - 128000·b - 1600·c = 160
- 2400000·a - 72000·b - 1200·c = 0
3*II - 4*I ; III - I
- 3200000·a - 32000·b = 160
2560000·a + 16000·b = - 80
2*II + I
1920000·a = 0 → a = 0
2560000·0 + 16000·b = - 80 --> b = -0.005
- 2400000·0 - 72000·(-0.005) - 1200·c = 0 --> c = 0.3
256000·0 + 4800·(-0.005) + 80·0.3 + d = 0 --> d = 0
Damit ist das Gleichungssystem gelöst.